WPC ^ Ivm/h'fRέa%T!ߑ{:&RA`Uk֩/TLOLo#\ì,i3q΃x5hзn<-{0 sԺgEug"[W! :w6Gެ4-@!o3Hխ E8'ZS+](m?[>sa~hk57~66yrk=w#Qf%Kdz:gU" %U%B 0I  CUfoaq B* B D+ 0 0EJ AY 1 ^ o {{ dw m n} 0r*#!N^ w@4  m!^ 8 1D 1u 0c@fa^ fa^ ^ ^ ^ ^ ^ ^ #f/a1^ E^ Q^ ]^ i^ u^ ^ ^ ^ fa^ ^ ^ ^ ^ ^ ^ ^ 'dx6dw^ /^ ;^ G^ S^ _^ kkkkkkkkkkkkkkkkkkkkkkkkkkk D3wNX9 ! C@\  `*Times New RomanTT4 2Quick A..0..dTable_A&0 d d d'dxd Level 1 Level 2 Level 3 Level 4 Level 5(e2Y.$ 9!  XLXX@XLXXXL  ($ (    )  M << deUU(EhCEKQW]cioAutoList21.1.1.1.1.1.1.1.00, qSiderealPeriodsubyears~=~1over{LBRACE1-1over{Synodic~Periodsubyears}RBRACE}~~,~~for~a~Superior~PlanetXX9SiderealXX9PeriodMMyearsXX&9d(XkXX 1XXXXH1XX X0OXX 1XXFqSynodicXX qPeriodMM7 3yearsXXAXX79,XX9forXX[9aXX9SuperiorXX+9Planet3|Pw NX9 ! C@XX@Q@(J9$  X XX@X XXX HP LaserJet 6P/6MP - Enhanced0AT) nopEqrstuEvEwt\$,PMU|S)(5hCEKQW]cioAutoList11.1.1.1.1.1.1.1.##37=CIQYag1.a.i.(1)(a)(i)1)a)(;3$2#  0  .3  0  TABLE AS)TABLE A}S)1S)US)S):S)aS)ȠS)Table_AȠS)ȠS)$S)%S)'S)S)u+*%S)٣S)(#/ tthePleiadesttAntarest t.t.Basedupontheprecedingtwoexperiments,explainexactlywhythereisa $)t$0 differencebetweenthesiderealandsynodicperiodsfortheMoon.'X XXX ԀThisistheanswertoquestion  *Z%1 _C#X XX'X #.u*@&2(#(# u__uu__uu_*@&2(#(#   +&'3 4.0  Explainhowthis2daydifferencewouldchangeiftheEarthtooklongertoorbittheSun.b(#(#    ` AnunderstandingofthedifferencebetweenthesynodicandthesiderealperiodsforthebrightplanetswasanessentialelementthatallowedtheGermanastronomer_Kepler_ԀtodiscoverhisLawsofPlanetaryMotion.5.0  SetStarryNighttonow,and_Centre_/LockontheSun.Enlargethefieldofviewto120o.Notice *z  theplanetVenusneartheSun,andMercurytotheeastoftheSun.RightclickonMercuryandselectit.StepbackwardorforwardintimebydaysuntilMercuryreachesitsmaximumangulardistanceeast(totheleft)fromtheSun.ThisiscalledGreatestEasternElongation,andisreadilyobservableintherealskyjustaftersunset.StepaheadorbackintimetodetermineyourbestestimateofthedateforthisfirstGEEofMercury.RecordthisdateasGEE1forMercuryinthetablebelow. (#(# Ѐ0  NowstepaheadandobserveMercuryasitswingsaroundtheSunontheWest,thenbackaroundtotheEast,thenreturnstoasecondGEE.RecordthatdateasGEE2inthetable.CalculatethesynodicperiodindaysbysubtractingthetwoJuliandates.Calculatethesynodicperiodinyearsbydividingthedaysby365.25.Lastly,usetheformulabelowtocomputethesiderealperiodofMercury. (#(# 0  ContinuesteppingaheaduntilVenusreachesGEE,thenperformthesamestepsabovetodeterminethesynodicperiodforVenus,bothindaysandinyears. (#(# *f d ddd dd dd 4dd 4$f %(#(#,eT$ ,4$ ,4$ ,4$ ,4$ ,4T +  3" p!  8xx3PLANET =,!!8!" =͐XX JULIANDATE !8" GEE1#X X͐'# =,!"#" =͐XX JULIANDATE !8$ GEE2 =,!"%" =SynodicPeriod(days)X X͐ =,!"'" =͐XX SynodicPeriod !8( (years)X X͐ =,!")" =͐XX SiderealPeriod !8* (years)X X͐ ND,"+" xx 8  qxxNMercury 'X$," ' 'X$-" ' 'X$." ' 'X$/" ' 'X$0" ' ?5X$1" xx q qxx?Venus '.&~!2" ' '.&~!3" ' '.&~!4" ' '.&~!5" ' '.&~!6" '-#!.&~!7" xx q  -BCYIEz hr p @Xdddddddd@EX)rSdTLX): ####(#(# X)$9#### DE_OKz|$r p @Xdddddddd@E)r>?K):6.0  Letusdeterminethesynodicperiodsforthreeofthesuperiorplanets.SetStarryNightto  December1,2001.RecordtheRA(hoursandminutes)andDEC(degrees)oftheSuninthetablebelow.ComputethepositionoftheantiSun.ThispositioninRAis12hoursahead(orbehind)theSun,andtheDECisoppositeinsign.Recordthispositioninthetablebelow. (#(#   *8f 9` ddeT$ e4$ 4$ 4$ 4$ 4T f (#(#,dd ,dd ,dd +  & . ~ & =,! " =RA =,! " =DEC 6,! " 6SUN ' \ " 'hm ' \ 3 'o󀀀 ' \ 3 'ANTISUNk '  " 'kk '  " 'kAX XhX hm#X XXAX 2#l '  3 'll '  3 'lFX XhX o󀀀#X XXFX ܡ3#" 3  "0  NowgrabthescreenandmoveituntiltheantiSolarpointisnearthecenterofthescreen.In[Settings,Planet/Sun]checkonEarth/Moontargets,andcheckoffEnlargemoonsize,thenOK.Asmallgreen bullseyewillappearonthescreen.Thismarkstheantisolarpoint. (#(# 0  NotethepositionsofSaturnandJupiterintheconstellationTaurus.Beginsteppingforwardintimebydays,andnoticethattheantiSunmovestowardsbothplanets.RecordtheJuliandatewhentheantiSunisclosesttoeachplanet.Thisplanetaryaspect,whentheplanetisnearesttotheantisolarpoint,isknownasopposition.Again,thisisaneasyobservationtomakeintherealsky,sincethesolarpositionforagivendateiswellknown (#(# ?X XXX 0  Nowsteponeyearahead,thenstepdaysaheaduntilSaturnandJupitercomeintoasecond ~ opposition.RecordtheseJuliandatesinthetablebelow#X XX?X 97#.d(#(# 0  SetthedatetoAugust1,2003,thenfindMars._Centre_/LockonMars.StepaheaduntiltheantiSunisclosesttoMars.RecordtheJuliandateforthisfirstoppositionofMarsinthetablebelow. (#(# 0  @X XXX Nowsteptwoyearsahead,thenstepdaysahead#X XX@X f9#untilMarscomesintoasecondopposition. 2 RecordthisJuliandateinthetablebelow.Foreachplanet,subtractthecorrespondingtwoJuliandatestocomputethesynodicperiodindays,thendivideeachby365.25tocomputethevaluesinyears.Lastly,computethesiderealperiodsforallthreeplanetsusingtheformulabelow. (#(# *-f .d ` ddd dd dd 8f 9(#(#,eT$ ,4$ ,4$ ,F4$ ,4$ ,4T +  3" `!$ 8xx3PLANET =,!!(%" =͐XX JULIANDATE !(& OPPOSITION1#X X͐<# =,!"'" =͐XX JULIANDATE !(( OPPOSITION2#X X͐=# =,!")" =͐XX SynodicPeriod !(* (days) =,!"+" =SynodicPeriod(years) =,!"-" =SiderealPeriod(years) I?,"/" xx 8  xxIX X͐6X XXX nJupitern#X XX6X ܪ?#1X XXX nn#X XX1X ?#oJX XXX Saturn#X XXJX O@#o 'H$0" ' 'H$1" ' 'H$2" ' 'H$3" ' 'H$4" ' :0H$5" xx qxx:=X XXX oSaturno#X XX=X ܙA#onnonGX XXX Jupiter#X XXGX B#IX XXX Ԁ#X XXIX NB#n '&n!6" ' '&n!7" ' '&n!8" ' '&n!9" ' '&n!:" ' ?5&n!;" xx q xx?3X XXX Mars#X XX3X ܘC# ''D#<" ' ''D#=" ' ''D#>" ' ''D#?" 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